lncdfn2 ============================================== Purpose ---------------- Computes natural log of interval of Normal cumulative distribution function. Format ---------------- .. function:: y = lncdfn2(x, dx) :param x: values at which to evaluate the cumulative distribution function. :type x: MxN matrix :param dx: ExE conformable with *x*, intervals used to compute the upper bound, *x + dx*. :type dx: KxL matrix :return lnp: the log of the integral from *x* to *x+dx* of the Normal distribution, i.e., .. math:: ln\ Pr(x < X < x+dx) :rtype lnp: max(M,K) x max(N,L) matrix Examples ---------------- :: // Set x x = -10; // Set interval dx = 29; print lncdfN2(x, dx); :: -7.6198530241605269e-24 :: // Set x x = 0; // Set interval dx = 1; print lncdfN2(x, dx); :: -1.0748623268620716e+00 :: // Set x x = 5; // Set interval dx = 1; print lncdfN2(x, dx); :: -1.5068446096529453e+01 Remarks ------- The relative error is: .. csv-table:: :widths: auto ":math:`\|x\| < 1`", "and", ":math:`dx < 1`", "±1e-14" ":math:`1 < \|x\| < 37`", "and", ":math:`\|dx\| < 1/\|x\|`", "±1e-13" ":math:`min(x,x+dx) > -37`", "and", ":math:`y > -690``", "±1e-11 or better" A relative error of ±1e-14 implies that the answer is accurate to better than ±1 in the 14th digit after the decimal point. Source ------ lncdfn.src .. seealso:: Functions :func:`cdfn2`